Gyroscopic Motion: Equations of Motion for the Two-Top

In the video ``The Mystery of Gyroscopic Motion: How Does It Do That?", I analyzed the physics of a simple spinning top constructed from two masses, called a ``two-top". I described in qualitative terms, and in detail, the forces that keep the two-top spinning and precessing. In this video I derive the equations of motion for the two-top using Lagrange multiplier methods. Simulations of the two-top's motion, and the accompanying forces, were created by solving these equations numerically. The computer code is called TwoTop, and is available at https://www.glowscript.org/#/user/jaydeebrown/folder/Public/program/TwoTop